NCERT Solutions for Class 10 Maths Chapter 8: Introduction to Trigonometry
Chapter 8 of Class 10 NCERT Maths opens the door to one of the most powerful mathematical tools ever developed — trigonometry. For many students, this is the first serious encounter with trigonometric ratios, and the initial impression can be intimidating. But once you understand the basic idea — that in a right-angled triangle, the ratios of any two sides depend only on the angle, not the size of the triangle — the whole chapter starts to make sense. The six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent form the backbone of this chapter. For other chapters of NCERT Solutions for Class 10 Maths, check NCERT Solutions for Class 10 and NCERT Solutions.
Chapter 8 also introduces the concept of trigonometric identities, which are equations that hold true for all values of the angle. These identities are used extensively in Chapter 9 and in higher mathematics. For CBSE Class 10 students, this chapter is pure gold — it is direct, formula-based, and highly predictable in board exams. Questions follow standard patterns, which means dedicated practice with Myclass24's NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry can genuinely help students score full marks in this section without much uncertainty.
Download PDF: NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry
Chapter 8 Introduction to Trigonometry – Ratios, Identities & Exercise Guide
The chapter moves from defining basic ratios to using them at standard angles, and then to proving identities. Each topic is tested in the NCERT exercises, and the progression is logical. Below is a chapter-specific breakdown to help students navigate the content effectively.
The Six Trigonometric Ratios (Right Triangle Context)
| Ratio | Definition | Reciprocal Of |
|---|---|---|
| sin θ | Opposite / Hypotenuse | cosec θ |
| cos θ | Adjacent / Hypotenuse | sec θ |
| tan θ | Opposite / Adjacent | cot θ |
| cosec θ | Hypotenuse / Opposite | sin θ |
| sec θ | Hypotenuse / Adjacent | cos θ |
| cot θ | Adjacent / Opposite | tan θ |
Standard Angle Values – The Most Important Table in Chapter 8
| Angle → | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | Not defined |
| cosec | Not defined | 2 | √2 | 2/√3 | 1 |
| sec | 1 | 2/√3 | √2 | 2 | Not defined |
| cot | Not defined | √3 | 1 | 1/√3 | 0 |
Exercise-wise Breakdown of Chapter 8
| Exercise | Topic | Questions | Focus Area |
|---|---|---|---|
| Exercise 8.1 | Trigonometric Ratios | 11 | Finding ratios from given sides, using Pythagoras |
| Exercise 8.2 | Standard Angle Values | 4 | Evaluating expressions using 0°, 30°, 45°, 60°, 90° |
| Exercise 8.3 | Complementary Angles | 7 | sin θ = cos(90°−θ) and related identities |
| Exercise 8.4 | Trigonometric Identities | 5 | Proving identities using sin²θ + cos²θ = 1 |
The Three Fundamental Trigonometric Identities
| Identity | Derived Form 1 | Derived Form 2 |
|---|---|---|
| sin²θ + cos²θ = 1 | sin²θ = 1 − cos²θ | cos²θ = 1 − sin²θ |
| 1 + tan²θ = sec²θ | tan²θ = sec²θ − 1 | sec²θ − tan²θ = 1 |
| 1 + cot²θ = cosec²θ | cot²θ = cosec²θ − 1 | cosec²θ − cot²θ = 1 |
One important observation about Exercise 8.3 — it introduces the idea of complementary angles, where sin of an angle equals cos of its complement. This means sin 30° = cos 60°, sin 45° = cos 45°, and so on. Board exams frequently use this relationship to simplify expressions. Myclass24's NCERT Solutions for Class 10 Maths Chapter 8 cover every such shortcut and identity proof in clear, sequential steps that match the CBSE answer format.